Vandermonde's identity

The Vandermonde’s identity or Vandermonde’s convolution, states that the binomial coefficient is the following property:

Story Proof

Consider a group of peacocks and toucans, from which a set of size birds will be chosen. There are possibilities for this set of birds. If there are peacocks in the set, then there must be toucans in the set. The right-hand side of Vandermonde’s identity sums up the cases for .

See Also

• convolution: one way to view the Vandermonde’s identity is as the discrete convolution where and .
• Pascal’s rule: